Using a confidence coefficient of 0.90, derive the interval estimate for homeowners that hold a home equity loan.

Question

In a recent poll of 2,000 homeowners, 1 in 8 homeowners reports having a home equity loan that they are currently paying off. Using a confidence coefficient of 0.90, derive the interval estimate for homeowners that hold a home equity loan.

Round intermediate calculations to at least 4 decimal places. Round “z” value and final answer to 3 decimal places.

Answer 1

Computation of 90% confidence interval for single proportion:

sample proportion (phat) = 1/8 = 0.125

sample size (n) = 2000

critical z value (z*) for 90% confidence interval = z-value for 95% = 1.645

CI = phat +/- z* * square root(phat * (1-phat)/n))